**READING: I §4 6**
Back to reading**:**
I §4 5

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*CHAPTER I* [:]
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Notions from Set Theory
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These pages can stand alone but it is best to have the book. topic index contents

Please read these notes from the beginning to here and then paragraph 5 of §4.

Before reading this page, please have another look at reading I §4 2 .

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ita-1-4-5-pg11
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The set of natural numbers can be used to give an easy definition of the notion of a sequence. A *sequence of n elements in a set X*, or an *n-tuple of elements of X*, may be defined to be a function from {1,2,...,n} into *X*; if the function is denoted *f* and we write *f*(1)=*x*, *f*(2)=*x*, ... *f*(n)=*x*, then the n-tuple is often written (*x*,*x*,...,*x*). An *infinite sequence of elements of X* (or a *sequence of elements of X* if there isn't any danger of confusion with finite sequences) is a function from the set of all natural numbers into *X*; as above this can be written (*x*,*x*,*x*,...), or, more conventionally, *x*,*x*,*x*,... or sometimes **.**

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